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BASIC ELECTRICAL INSTALLATION WORK
Fig. 2.13 Characteristics of a sine wave.
Fig. 2.14 Sinusoidal waveform showing instantaneous values of voltage.
Cable and equipment insulation levels must be equal to or greater than this value. The average value is the average over one half-cycle of the instantaneous values as they change from zero to a maximum and can be found from the following formula applied to the sinusoidal waveform shown in Fig. 2.14: Vav
V1 V2 V3 V4 V5 V6 6
Vrms
V12 V22 V32 V42 V52 V62
0.7071 Vmax
6
For any sinusoidal waveform the rms value is equal to 0.7071 of the maximum value.
0.637 Vmax
For any sinusoidal waveform the average value is equal to 0.637 of the maximum value. The rms value is the square root of the mean of the individual squared values and is the value of an a.c. voltage which produces the same heating effect as a d.c. voltage. The value can be found from the following formula applied to the sinusoidal waveform shown in Fig. 2.14.
EXAMPLE The sinusoidal waveform applied to a particular circuit has a maximum value of 325.3 V. Calculate the average and rms value of the waveform. average value Vav 0.637 Vmax Vav 0.637 325.3 207.2 V rms value Vrms 0.7071 Vmax Vrms 0.7071 325.3 230 V